If `(h ,k)` is a point on the axis of the parabola `2(x-1)^2+2(y-1)^2=(x+y+2)^2` from where three distinct normals can be drawn, then prove that `h > 2.`

If (h,k) is a point on the axis of the parabola 2{(x-1)^2 + (y-1)^2} = (x+y)^2 from where three distinct normal can be drawn, then the least integral value of h is :

Find the point on the axis of the parabola 3y^2+4y-6x+8 =0 from where three distinct normals can be drawn.

The set of points on the axis of the parabola (y-2)^2=4(x-1/2) from which three distinct normals can be drawn to the parabola are

The set of points on the axis of the parabola (x-1)^(2)=8(y+2) from where three distinct normals can be drawn to the parabola is the set (h,k) of points satisfying

The set of points on the axis of the parabola (x-1)^2=8(y+2) from where three distinct normals can be drawn to the parabola is the set (h ,k) of points satisfying (a)h >2 (b) h >1 (c)k >2 (d) none of these

The set of points on the axis of the parabola y^2 =4ax , from which three distinct normals can be drawn to theparabola y^2 = 4ax , is

The set of points on the axis of the parabola y^2-4x-2y+5=0 from which all the three normals to the parabola are real , is

The equation to the normal to the parabola x^(2) = 2y at (1, 2) is

Statement I two perpendicular normals can be drawn from the point (5/2,-2) to the parabola (y+1)^2=2(x-1) . Statement II two perpendicular normals can be drawn from the point (3a,0) to the parabola y^2=4ax .

Column I, Column II Points from which perpendicular tangents can be drawn to the parabola y^2=4x , p. (-1,2) Points from which only one normal can be drawn to the parabola y^2=4x , q. (3, 2) Point at which chord x-y-1=0 of the parabola y^2=4x is bisected., r. (-1,-5) Points from which tangents cannot be drawn to the parabola y^2=4x , s. (5,-2)